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Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets

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  • J. P. Bouchaud

    (Service de Physique de l'Etat Condensé, (Also at: Science et Finance, 109-111 rue V. Hugo, 92 532 Levallois, France) CEA, Orme des Merisiers, 91 191 Gif sur Yvette CEDEX, France)

  • D. Sornette

    (Laboratoire de Physique de la Matière Condensée, Université de Nice-Sophia Antipolis B. P. 70, Parc Valrose, 06108 Nice CEDEX 2, France)

  • C. Walter

    (Direction de la Gestion et des Relations Investisseurs- BC 11152 Crédit Lyonnais, 19, Boulevard des Italiens, 75002 Paris, France)

  • J. P. Aguilar

    (Capital Futures Management, 109-111 rue Victor Hugo, 92932 Levallois CEDEX, France)

Abstract

We propose a method of optimization of asset allocation in the case where the stock price variations are supposed to have "fat" tails represented by power laws. Generalizing over previous works using stable Lévy distributions, we distinguish three distinct components of risk described by three different parts of the distributions of price variations: unexpected gains (to be kept), harmless noise inherent to financial activity, and unpleasant losses, which is the only component one would like to minimize. The independent treatment of the tails of distributions for positive and negative variations and the generalization to large events of the notion of covariance of two random variables provide explicit formulae for the optimal portfolio. The use of the probability of loss (or equivalently the Value-at-Risk), as the key quantity to study and minimize, provides a simple solution to the problem of optimization of asset allocations in the general case where the characteristic exponents are different for each asset.

Suggested Citation

  • J. P. Bouchaud & D. Sornette & C. Walter & J. P. Aguilar, 1998. "Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 25-41.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:01:n:s0219024998000035
    DOI: 10.1142/S0219024998000035
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    Cited by:

    1. Christian Walter, 2020. "Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections," Sustainability, MDPI, vol. 12(18), pages 1-28, September.
    2. J. V. Andersen & D. Sornette, 1999. "Have your cake and eat it too: increasing returns while lowering large risks!," Papers cond-mat/9907217, arXiv.org.
    3. Y. Malevergne & D. Sornette, 2001. "General framework for a portfolio theory with non-Gaussian risks and non-linear correlations," Papers cond-mat/0103020, arXiv.org.
    4. Y. Malevergne & D. Sornette, 2003. "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions," Papers physics/0301009, arXiv.org.
    5. D. Sornette & P. Simonetti & J.V. Andersen, 1999. ""Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions," Finance 9902004, University Library of Munich, Germany.
    6. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    7. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    8. Spencer Wheatley & Annette Hofmann & Didier Sornette, 2021. "Addressing insurance of data breach cyber risks in the catastrophe framework," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(1), pages 53-78, January.
    9. Y. Malevergne & D. Sornette, 2002. "Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous markets," Papers cond-mat/0207475, arXiv.org.
    10. Mihail Turlakov, 2016. "Leverage and Uncertainty," Papers 1612.07194, arXiv.org.

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